Semester One 2019Examination Period

Faculty of Business and Economics

EXAM CODES: ETC1010

TITLE OF PAPER: DATA MODELLING AND COMPUTING - Paper 1

EXAM DURATION: 2 hours writing time

READING TIME: 10 minutes

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InstructionsThere are 9 questions worth a total of 100 marks. You should attempt all of the questions.

QUESTION 1

This question is about tidy data.

species location class countemu wilsons prom aves 40emu grampians aves 20

wombat wilsons prom mammalia 30wombat grampians mammalia 10wallaby wilsons prom mammalia 50wallaby grampians mammalia 50

(a) There are three variables in this data set. Explain why this is, that is, why count is not considereda variable.

[3 marks]

What was measured at each wildlife sighting was species, class and location. Count is a statisticthat was computed after the complete data set was collected, and provides a convenient way tostore the data with less rows.

(b) There are 200 observations in the data. Explain why, that is, why the answer is not 6.[3 marks]

There were 200 wildlife sightings in the data. The 6 rows is a tabular summary of the combinationsof levels of the observed variables.

(c) What type of variable would location be considered to be, and what type of format would it betreated as in R? (Circle two, one from each line)

[3 marks]

quantitative qualitative temporal spatial

qualitative

numeric double logical character ordered factor

character

[Total: 9 marks]

— END OF QUESTION 1 —

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QUESTION 2

This question is about data wrangling.

For each of these questions, write down the verbs that you would need to use to do the calculations toanswer it using the nycflights13 data. Add explanations of why you would approach it that way if youfeel it is necessary.

> glimpse(flights)Observations: 336,776Variables: 15$ year <int> 2013, 2013, 2013, 2013, 2013, 2013, 2013, 2013, 2013...$ month <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1...$ day <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1...$ dep_time <int> 517, 533, 542, 544, 554, 554, 555, 557, 557, 558, 55...$ dep_delay <dbl> 2, 4, 2, -1, -6, -4, -5, -3, -3, -2, -2, -2, -2, -2,...$ arr_time <int> 830, 850, 923, 1004, 812, 740, 913, 709, 838, 753, 8...$ arr_delay <dbl> 11, 20, 33, -18, -25, 12, 19, -14, -8, 8, -2, -3, 7,...$ carrier <chr> "UA", "UA", "AA", "B6", "DL", "UA", "B6", "EV", "B6"...$ flight <int> 1545, 1714, 1141, 725, 461, 1696, 507, 5708, 79, 301...$ tailnum <chr> "N14228", "N24211", "N619AA", "N804JB", "N668DN", "N...$ origin <chr> "EWR", "LGA", "JFK", "JFK", "LGA", "EWR", "EWR", "LG...$ dest <chr> "IAH", "IAH", "MIA", "BQN", "ATL", "ORD", "FLL", "IA...$ air_time <dbl> 227, 227, 160, 183, 116, 150, 158, 53, 140, 138, 149...$ distance <dbl> 1400, 1416, 1089, 1576, 762, 719, 1065, 229, 944, 73...$ hour <dbl> 5, 5, 5, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6...

(i) What is the typical daily number of flights that United flies out of JFK between 8am and 9am?[3 marks]

filter records to only keep United flights, for JFK between 8-9am, summarise to compute theaverage number of flights.

(ii) What hour of day should you plan to fly if you want to avoid delays as much as possible?[3 marks]

group by hour, summarise to compute average delay, and then arrange by lowest to highest.

(iii) What plane (identified by their tail number) is responsible for the most delays?[3 marks]

group by tailnum, summarise to compute average delay, and then arrange from highest to lowest

(iv) How do high winds impact flight operations at Newark airport?[3 marks]

Can’t be done with this table alone. Or the list of verbs provided! It would need to join theweather table, which does exist on the data set, with this data.

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Full verb list: filter, select, mutate, summarise, arrange, group_by, near, desc, starts_with,ends_with, contains, matches, rename, top_n, first, min_rank, lag, cumsum, count, tally

[Total: 12 marks]

— END OF QUESTION 2 —

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QUESTION 3

This question is about visualisation.

The hierarchy of mapping quantitative variables to plots, in order to return an accurate reading is asfollows:Mapping Rank ExampleArea 4 mosaic plotShading, color 6 choropleth mapPosition - nonaligned scale 2 side-by-side boxplot to com-

pare the boxesVolume, curvature 5 3D bubble charts??Position - common scale 1 scatterplotLength, direction, angle 3 piechart

(a) Fill in the rank column, labelling the the mappings 1 through 7, with 1 indicating this is themapping method that analysts can most accurately read off the data values.

[4 marks]

(b) Given a plot type example, or a ggplot geom would also be acceptable, for each mapping. Writethis into the third column.

[4 marks]

(c) The facetting in this plot may make some comparisons between groups difficult to make becauseof what cognitive perception issue. (Circle one)

[2 marks]

proximity colour blindness change blindness pre-attentive layering

change blindness

(d) Which variable(s) would be most affected by this? (Circle)[2 marks]

gender age year

gender and age

[Total: 12 marks]

— END OF QUESTION 3 —

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QUESTION 4

This question is about handling missing values.

(a) TRUE or FALSE: The shadow matrix can be thought of as a data table indicating where theoriginal values are missing. TRUE

[2 marks]

(b) TRUE or FALSE: When you have missing values in a data table, it is reasonable to drop theobservation before conducting your analysis. FALSE

[2 marks]

(c) Which method for imputing missing values is better in this scenario? (Circle one)[3 marks]

There is a relationship between the variables, and all are quantitative. Several of the variableshave missing values.

(i) use the mean of the complete values, separately for each variable.(ii) set up several regression models, using the variable with missings as the response, and usecomplete cases to estimate.(iii) simulate values from a normal distribution for each variable, using the mean and standarddeviation of the complete cases.

ii

(d) Use the following regression model set up to impute the missing value on number of bedrooms,using complete information on number of rooms, for the Melbourne house price data, for thisobservation, Rooms = 8. Bedroom=NA.

[3 marks]

Coefficients:(Intercept) Rooms

0.08523 0.96727

7.8

[Total: 10 marks]

— END OF QUESTION 4 —

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QUESTION 5

This question is about model fitting and optimisation.

This is a simulated data set, with values generated by the code below.

library(tidyverse)square_err <- function(par, data) {

sq <- sum((data$y-(par[1]+par[2]*data$x+par[3]*data$x^2+par[4]*data$x^3+par[5]*data$x^4))^2)

return(sq)}x <- runif(200, -1, 2)df <- tibble(x, y=-5+4*x-6*x^2-2*x^3+3*x^4+rnorm(200)*0.5)ggplot(df, aes(x=x, y=y)) + geom_point()

fit <- optim(c(1,1,1,1,1), square_err, data=df))

(a) Write down the true regression coefficients used to generate the data.[4 marks]

(-5,4,-6,-2,3)

(b) The fitted model has these coefficients:

> fit$par[1] -4.992065 3.901229 -6.064781 -1.844502 2.968980

Why is there a difference from the parameters used to generate the data?[3 marks]

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(These are computed on a sample of data so they are close to the parameter values but will neverbe exactly identical. )

(c) Write down the equation of the fitted model.[4 marks]

y = 4.992065 + 3.901229x− 6.064781x2 − 1.844502x3 + 2.968980x4

(d) Predict the response value for x = 2.[4 marks]

21.3

(e) If the observed value for x = 2 is 10, compute the residual for the fit.[3 marks]

11.3

(f) Why is the fitted value so much different from the observed value? Is this correct, or has therebeen a mistake? Explain.

[3 marks]

Nonlinear functions can change dramatically with small changes in the coefficients. There hasbeen no mistake made, but the coefficients do vary a little from the true values, and this leads toquite a large discrepancy in this area of the predictor.

[Total: 21 marks]

— END OF QUESTION 5 —

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QUESTION 6

This question is about linear regression.

A simulated data set has two predictors, x1, x2 and one response variable (y), where x2 is a categoricalpredictor with two levels, A,B. Below are summaries of two different model fits to the data.

Model I:term estimate std.error statistic p.value

1 (Intercept) 6.35 0.09 70.55 0.002 x_1 -1.65 0.08 -21.18 0.003 x_2B 3.02 0.14 22.21 0.00

Model II:term estimate std.error statistic p.value

1 (Intercept) 6.03 0.05 115.15 0.002 x_1 -1.03 0.05 -19.78 0.003 x_2B 4.01 0.09 44.96 0.004 x_1:x_2B -1.96 0.09 -20.98 0.00

r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC deviance df.residualI 0.83 0.83 0.92 477.50 0.00 3 -264.77 537.55 550.74 165.37 197

II 0.95 0.95 0.51 1174.48 0.00 4 -147.06 304.12 320.61 50.96 196

(a) This is the equation for the fitted model I. There’s a mistake, please fix it.[2 marks]

y = 6.35− 1.65x1 if x2 = A

= 3.33− 1.65x1 if x2 = B

It should be y

(b) Write down the equation for model 2, as simply as you can.[3 marks]

y = 6.03− 1.03x1 if x2 = A

= 10.04− 2.99x1 if x2 = B

(c) Make a sketch of each model. Be sure to label your axes of the plots for the predictors and theresponse.

[4 marks]

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(d) Which model fits the data better? Why?[3 marks]

II, because R2 is higher and deviance is smaller.

[Total: 12 marks]

— END OF QUESTION 6 —

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QUESTION 7

This question is about text analysis.

(a) For this sentence:

Emma Woodhouse, handsome, clever, and rich, with a comfortable home.

(a) Indicate how it would be tokenised, for example using code like unnest_tokens(word, text).[3 marks]

Emma/ Woodhouse/ handsome/ clever/ and/ rich/ with/ a/ comfortable/ home

(b) Mark the words that would typically be considered to be "stop words".[3 marks]

and with a

(b) Fill in the blank, from the word bank provided:[3 marks]

The statistic "term frequency, inverse document frequency", is intended to measure howa word is to a document in a collection (or corpus) of documents,

important different frequent relatively frequent common

relatively frequent

[Total: 9 marks]

— END OF QUESTION 7 —

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QUESTION 8

This question is about generating networks and their analysis.

(a) For the network visualisation show below, write down what the association matrix might be,using numbers.

[3 marks]

0 0 0 0 10 0 0 1 00 0 0 1 10 0 0 0 00 0 0 1 0

(b) For the association matrix below, showing the number of times that these five people havemessaged each other in the last week.

Meg Tay Yat Zili JessMeg 0.00 5.00 4.00 1.00 1.00Tay 5.00 0.00 4.00 2.00 1.00Yat 4.00 4.00 0.00 0.00 0.00Zili 1.00 2.00 0.00 0.00 6.00Jess 1.00 1.00 0.00 6.00 0.00

(a) Which two people would be considered to be most similar (most connected)? Meg, Tay[3 marks]

(b) Draw the network diagram, if you consider closeness (edges to be connected) to be 4 or more.[3 marks]

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[Total: 9 marks]

— END OF QUESTION 8 —

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QUESTION 9

This question is about data collection practices.

In 2008, IBM, the most venerable computer (now data analysis) company declared vegemite to be theworld’s most recognisable brand.

Research conducted by IBM showed that Vegemite outranked other giants like Coca Cola, Nike, Toyota,Sony and Starbucks when it came to people searching and commenting on their favourite product online.The study, which examined more than 1.5b posts in 38 different languages, showed 479,206 mentions ofVegemite - more than any other brand globally.

(a) TRUE or FALSE: IBM used random sampling to collect their data.[2 marks]

FALSE

(b) Explain why these survey results might not be an accurate summary of global brand recognition.[4 marks]

Its studying only posts in online forums. Only some people participate in these, so the informationmay not be representative of the global community.

[Total: 6 marks]

— END OF QUESTION 9 —

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